In 1997, ABC Corporation had sales of Rs.70000 and had a profit of Rs.3500. The Corporation profit in 2000 was what percent of its sales in 2000? I. The difference between sales and profit in 2000 was 20% greater than the difference between sales and profit in 1997. II. Sales and profit in 2000 each increased by 20% over sales and profit in 1997.
A :
If the question can be answered by using any of the statements alone, but not by using
the other statement alone.
B :
If the question can be answered by using either of the statements alone.
C :
If the question can be answered only by using both the statements together.
Answer: A Statement I gives the following equation for 2000 sales: Profit + 66500 × 120/100 I alone is not sufficient. Statement II allows us to calculate actual sales and profit values in 2000, and thus the sales/profit ratio.
Q. No. 152:
If |x| > 2 and x is an integer, then what is the value of x? I. x is a negative number II. x2 + x – 12 < 0
A :
If the question can be answered by using any of the statements alone, but not by using
the other statement alone.
B :
If the question can be answered by using either of the statements alone.
C :
If the question can be answered only by using both the statements together.
Answer: B x is an integer. Statement (I) does not give the definite value of x, hence it alone is not sufficient. Statement (II) gives, (x – 3)(x + 4) < 0 =>–4 < x < 3 ⇒ x = –3. Statement (II) alone is sufficient to answer the question.
Q. No. 153:
What is the difference of the cubes of two numbers? I. products of the numbers is 16. II. difference of the numbers is 10.
A :
If the question can be answered by using any of the statements alone, but not by using the other statement alone.
B :
If the question can be answered by using either of the statements alone.
C :
If the question can be answered only by using both the statements together.
Answer: C Statement (I) : Let the two numbers be a and b and a > b. Then, ab = 16. Statement (II): a – b = 10. Both the statements alone are not sufficient to answer the question. Combining both: We know that, a3 - b3 = (a-b)3 - 3ab(a-b) i.e., we can answer the question combining both the statements.
Q. No. 154:
If K is a positive integer less than 10 and N = 4321 + K, what is the value of K? I. N is divisible by 3. II. N is divisible by 7.
A :
If one statement alone is sufficient, but the other statement is not sufficient to answer the question.
B :
If both statement I and II together are sufficient to answer the question, but neither statement alone is sufficient.
C :
If each statement alone is sufficient to answer the question.
D :
If statement I and II together are not sufficient to answer the question.
Answer: A N = 4321 + K where 0 < K < 10 ⇒ positive integer By statement 1, N is divisible by 3 , K = 2 or 5 or 8. No unique answer. By statement 2, N is divisible by 7 , N = 4321 + 5 = 4326 which is divisible by 7 => K = 5 Thus, statement II alone is sufficient to answer.
Q. No. 155:
The surface area of a square tabletop was changed such that, one of the dimensions was reduced by 1 inch and the other dimension was increased by 2 inches. What was surface area before these changes were made? I. After the changes were made, the surface area was 70 sq. inches. II. There was a 25 percent increase in one of the dimensions.
A :
If one statement alone is sufficient, but the other statement is not sufficient to answer the question.
B :
If both statement I and II together are sufficient to answer the question, but neither statement alone is sufficient.
C :
If each statement alone is sufficient to answer the question.
D :
If statement I and II together are not sufficient to answer the question.
Answer: C Let the side of the square be x Area is x^2 Side reduced by 1 inch i.e x – 1 Side increased by 2 inches i.e x + 2 According to statement 1, the area of the figure after the change is 70 sq. inches. => (x – 1)(x + 2) = 70 => x = 8 inches ∴ Area = x^2 = 64 sq. inches. Thus, statement I alone is sufficient to answer the question. From statement II, there is an increase of 25% in one of the dimensions. One side is increased by 2 inches. => 0.25x = 2 x = 8 inches and x2 = 64 sq. inches Statement II alone is sufficient to answer the question.
Q. No. 156:
What was the total number of trips to a certain construction site made by two trucks to carry 18 metric tons of gravel? I. The smaller truck carried 5 metric tons of gravel on each trip to the site and the larger truck carried 8 metric tons of gravel on each trip to the site. II. Each truck delivered the same total amount of the gravel to the site.
A :
If one statement alone is sufficient, but the other statement is not sufficient to answer the question.
B :
If both statement I and II together are sufficient to answer the question, but neither statement alone is sufficient.
C :
If each statement alone is sufficient to answer the question.
D :
If statement I and II together are not sufficient to answer the question.
Answer: A Let the number of trips made by small truck be S and big truck be B. S + B = ? Statement I: Small truck in one trip carries 5 metric tons and big truck carries 8 metric tons. => Total material carried = S × 5 + B × 8 Statement I above is enough, taking S = 2 and B = 1, 5S + 8B = 5(2) + 8(1) = 18 metric tons. Statement II: Each truck delivered the same total amount of gravel ⇒ x mt To find the total trips, statement II alone is not sufficient. Statement 1 alone is sufficient